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UBC Theses and Dissertations

A search for UV excess objects in the direction of the globular cluster NGC 6121 (M4) Chan, Edmond 1984

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A SEARCH FOR UV EXCESS OBJECTS IN THE DIRECTION OF THE GLOBULAR CLUSTER NGC 6121 (M4) by EDMOND £HAN B . S c , U n i v e r s i t y of B r i t i s h Columbia, 1981 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE FACULTY OF GRADUATE STUDIES Geophysics and Astronomy We accept t h i s t h e s i s as conforming to the r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA August 1984 © Edmond Chan, 1984 6 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the The U n i v e r s i t y of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and study. I f u r t h e r agree that p e r m i s s i o n f o r e x t e n s i v e copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s or her r e p r e s e n t a t i v e s . I t i s understood that copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain s h a l l not be allowed without my w r i t t e n p e r m i s s i o n . Department of Geophysics and Astronomy The U n i v e r s i t y of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date: August 1984 ABSTRACT A b l i n k survey was performed on a 50' diameter f i e l d c e n t e r e d about the g l o b u l a r c l u s t e r M4. The purpose was to s e l e c t out p o s s i b l e c l u s t e r white dwarfs and UV excess QSOs in the f i e l d . A t o t a l of 1096 o b j e c t s b r i g h t e r than U = 22.3 were found i n the region between 3.9' and 23.7' from the c l u s t e r c e n t e r . S u b t r a c t i o n of the expected background r e v e a l e d an obvious c o n c e n t r a t i o n of the o b j e c t s towards the center of the c l u s t e r . The r a d i a l gradient matches w e l l with that o b t a i n e d by King et a l . (1968) f o r t h e i r s t a r counts i n M4. T h i s g i v e s a lower l i m i t of =* 240 white dwarfs in M4 b r i g h t e r than M^ . 11. Photometry of 74 of the o b j e c t s which were v i s i b l e on both the b l i n k e d U and B p l a t e s y i e l d e d 9 o b j e c t s with c o l o u r s and photometric p a r a l l a x e s expected f o r c l u s t e r white dwarfs. F i v e of these have M^ . < 8.5, assuming that they are indeed in the c l u s t e r . Comparisons of these numbers have been made with t h e o r e t i c a l estimates from F u s i - P e c c i and Re n z i n i (1979) and from H i l l s (1974) and were not found to be i n c o n s i s t e n t with the p r e d i c t i o n s . A t o t a l of 37 UV excess QSOs were a l s o i d e n t i f i e d on the b a s i s of t h e i r c o l o u r s . T h e i r i n t e g r a t e d s u r f a c e d e n s i t i e s from B 0 = 19.5 to B 0 = 21.5 correspond w e l l with the pure l u m i n o s i t y e v o l u t i o n model of B r a c e s s i et a l . (1980). Table of Contents ABSTRACT i i L i s t of Tables v L i s t of F i g u r e s v i Acknowledgments . v i i 1 . INTRODUCTION 1 2. OBSERVATIONAL MATERIAL AND DATA REDUCTION 4 2.1 O b s e r v a t i o n a l Data 4 2.2 The B l i n k Survey 5 2.3 Photograhic Photometry 6 2.3.1 Photometric Standards 6 2.3.2 The PDS Data 9 2 . 4 Reductions 11 2.4.1 Aperture Photometry 11 2.4.2 Photometry by S t e l l a r P r o f i l e F i t t i n g 14 2 . 5 C a l i b r a t i o n 15 2.6 Colour Terms 24 2.7 R e s u l t s of the Photometry 25 3. WHITE DWARFS IN M4 30 3.1 R e s u l t s of the B l i n k Survey 30 3.2 Photometric White Dwarf Candidates 35 3.3 D i s c u s s i o n of the R e s u l t s 40 4. UV EXCESS QUASARS IN THE DIRECTION OF M4 44 4.1 S e l e c t i o n of the QSO sample 44 4.2 D i s c u s s i o n of the R e s u l t s 45 5. CONCLUSIONS 48 BIBLIOGRAPHY 51 i i i APPENDIX I: ESTIMATE OF THE WD FOREGROUND 53 APPENDIX I I : FINDING CHARTS FOR THE PHOTOMETERED CANDIDATES 56 i v L i s t of Tables I L i s t of Photographic P l a t e s 4 II CCD Standards 7 III S t a t i s t i c s of C a l i b r a t i o n Curves 24 IV Colour Transformation C o e f f i c i e n t s 25 V Photometric WD and QSO Candidates i n M4 27 VI Blue o b j e c t r a d i a l d i s t r i b u t i o n about M4 30 VII Background c o r r e c t e d blue o b j e c t d i s t r i b u t i o n s 33 VIII P r e d i c t e d Number of White Dwarfs i n M4 (FPR) 42 IX P r e d i c t e d Number of White Dwarfs i n M4 ( H i l l s ) 43 X QSO Candidate Number D i s t r i b u t i o n 45 v L i s t of F i g u r e s 1 U P l a t e Flux C a l i b r a t i o n Curve 18 2 B P l a t e Flux C a l i b r a t i o n Curve . 19 3 V P l a t e Flux C a l i b r a t i o n Curve 20 4 U P l a t e R a t i o C a l i b r a t i o n Curve 21 5 B P l a t e R a t i o C a l i b r a t i o n Curve 22 6 V P l a t e R a t i o C a l i b r a t i o n Curve 23 7 R a d i a l Blue Object D i s t i b u t i o n 32 8 R a d i a l Star and C o r r e c t e d Object D i s t r i b u t i o n s 34 9 • C o l o u r - C o l o u r Diagram for Photometered Candidates ..36 10 Colour-Magnitude Diagram of M4 38 11 QSO I n t e g r a t e d Surface D e n s i t i e s 46 12 F i n d i n g Chart A 58 13 F i n d i n g Chart B 60 14 F i n d i n g Chart C 62 15 F i n d i n g Chart D 64 16 F i n d i n g Chart E 66 17 L o c a t i o n of the F i n d i n g Charts A - E 68 v i Acknowledgments I would l i k e to thank my s u p e r v i s o r , Dr. H. Richer, f o r h i s p a t i e n c e , guidance, and support over the d u r a t i o n of the re s e a r c h . I am a l s o g r a t e f u l to Dr. J . Hesser f o r o b t a i n i n g two of the photograhic p l a t e s used i n t h i s study. John N i c o l and Dr. D. Crabtree have been most h e l p f u l i n both dev e l o p i n g and e x p l a i n i n g some of the necessary software f o r the r e d u c t i o n s and I give them my s p e c i a l thanks. I would a l s o l i k e to thank the Astronomy graduate students f o r t h e i r d i s c u s s i o n s and a d v i c e , as w e l l as the t i m e l y supply of an o c c a s s i o n a l l y needed program. My thanks go as w e l l to the f a c u l t y f o r making graduate l i f e an enjoyable experience. And l a s t , but not l e a s t , I extend much g r a t i t u d e to my fa m i l y and f r i e n d s who have o f f e r e d t h e i r moral support and encouragement throughout my s t u d i e s . v i i Chapter 1 INTRODUCTION Gl o b u l a r c l u s t e r s p l a y an important r o l e i n the development of t h e o r i e s of s t e l l a r e v o l u t i o n . Indeed, the colour-magnitude diagrams of g l o b u l a r c l u s t e r s serve as a b a s i s f o r the mod e l l i n g of the e v o l u t i o n of main sequence dwarfs i n t o red g i a n t s and h o r i z o n t a l branch s t a r s . However, the d e t a i l s of the development of the s t a r s at the t i p of the asymptotic g i a n t branch i n t o the r e g i o n of the white dwarfs remains vague. The appearance of the colour-magnitude diagrams of g l o b u l a r c l u s t e r s would appear to i n d i c a t e that s t e l l a r e v o l u t i o n at t h i s stage i s r a p i d ; and hence, o b s e r v a t i o n s of s t a r s i n t r a n s i t i o n between g i a n t s and white dwarfs are expected to be r a r e . C e n t r a l s t a r s of p l a n e t a r y nebulae may be examples of such o b j e c t s . Because of t h i s p a u c i t y of i n f o r m a t i o n a r r i v i n g from d i r e c t o b s e r v a t i o n s , a more i n d i r e c t approach must be used i f i n v e s t i g a t i o n s of white dwarf pr o d u c t i o n are to be undertaken. For i n s t a n c e , a knowledge of the white dwarf p o p u l a t i o n i n g l o b u l a r c l u s t e r s would be v a l u a b l e i n that i t i s e s s e n t i a l data when c o n s i d e r i n g the r a t e s of white dwarf formation out of the g i a n t branch, the mass l o s s r a t e s f o r g i a n t s ; and hence, the low mass s t a r c o n t r i b u t i o n to the chemical enrichment of the Galaxy. I n v e s t i g a t i o n s of white dwarfs i n g l o b u l a r c l u s t e r s would a l s o f u r n i s h much needed o b s e r v a t i o n a l c o n s t r a i n t s on t h e o r e t i c a l white dwarf l u m i n o s i t y f u n c t i o n s and c o o l i n g times. Indeed, s i n c e the e x i s t e n c e of a white dwarf 1 2 component i n g l o b u l a r c l u s t e r s i s a foregone c o n c l u s i o n of the present s t e l l a r e v o l u t i o n a r y models, attempts to v e r i f y t h i s p r e d i c t i o n are e s s e n t i a l to the c o n f i r m a t i o n of the b a s i c t h e o r y . I t i s a p a r t i c u l a r l y d i s t r e s s i n g f a c t , however, that the realm of the g l o b u l a r c l u s t e r s l i e s u f f i c i e n t l y f a r away to g e n e r a l l y r e s t r i c t s t u d i e s of t h e i r white dwarf content. An attempt has been made by Ri c h e r (1978a, 1978b) to l o c a t e white dwarfs i n NGC 6752. A t o t a l of 10 white dwarf c a n d i d a t e s were found i n the f i e l d on the b a s i s of t h e i r c o l o u r s . Four of these have been confirmed s p e c t r o s c o p i c a l l y (Richer 1979). The open c l u s t e r M67 was i n v e s t i g a t e d by Racine (19 71) and was found devoid of a white dwarf p o p u l a t i o n . T h i s intermediate age c l u s t e r resembles a g l o b u l a r i n morphology and i t s r e l a t i v e p r o x i m i t y to the Sun pe r m i t t e d the search f o r white dwarfs with M^ . < 12.2. The absence of white dwarfs i n t h i s c l u s t e r , although d i s a p p o i n t i n g , may not be t o t a l l y unexpected s i n c e M67 i s poorer i n s t e l l a r content than a t y p i c a l g l o b u l a r . M67 a l s o l a c k s a w e l l d e f i n e d h o r i z o n t a l branch; the s t a r s of which, are thought to evolve i n t o the asymptotic g i a n t branch — the assumed l o c u s of the p r e c u r s o r s to white dwarfs. Other open c l u s t e r s t u d i e s have a l s o been c a r r i e d out and are summarized i n Anthony-Twarog (1982). The major t h r u s t of these s t u d i e s i s an attempt to a s c e r t a i n the upper l i m i t to the p r o g e n i t o r masses of the white dwarfs, s i n c e the younger the c l u s t e r that c o n t a i n s white dwarfs, the more 3 massive the s t a r s must have been that produced them. T h i s approach i s l e s s s u i t a b l e f o r g l o b u l a r c l u s t e r s t u d i e s s i n c e a l l the g a l a c t i c g l o b u l a r s are of the order 10 1° years o l d and t h e r e f o r e have white dwarf p r o g e n i t o r masses l e s s than a s o l a r mass. However, the advantage of g l o b u l a r c l u s t e r s t u d i e s i s i n the p r o d i g i o u s numbers of white dwarfs that may be d e t e c t e d i n c o n j u n c t i o n with the w e l l developed and populated morphologies of the c l u s t e r colour-magnitude diagrams; thereby, p r o v i d i n g a s u b s t a n t i a l s t a t i s t i c a l b a s i s not a v a i l a b l e i n the s t u d i e s of open c l u s t e r s . Such numbers are r e q u i r e d i n order to pursue the d e t a i l s of s t e l l a r e v o l u t i o n and g a l a c t i c chemical enrichment as noted above. I t i s c l e a r , then, that the f i r s t step i s to secure a sample of white dwarfs. I t i s t h e r e f o r e the primary purpose of t h i s t h e s i s to attempt to l o c a t e c l u s t e r white dwarf candidates belonging to NGC 6121 (M4), the c l o s e s t g l o b u l a r c l u s t e r ( (m - M ) v - 12.5, Richer and Fahlman 1984, and Lee 1977). A secondary g o a l , a consequence of the search technique employed, i s to f i n d p o s s i b l e UV excess QSO c a n didates which happen to be in the f i e l d of M4. These o b j e c t s can then be used as a measure of the QSO background s u r f a c e d e n s i t i e s to v a r i o u s l i m i t i n g magnitudes — p r o v i d i n g f u r t h e r o b s e r v a t i o n a l data i n the quest to a s c e r t a i n the mode of the e v o l u t i o n of the quasar p o p u l a t i o n . Chapter 2 OBSERVATIONAL MATERIAL AND DATA REDUCTION 2.1 OBSERVATIONAL DATA A t o t a l of 5 wide f i e l d photographic p l a t e s of M4 were obtained in the UBV system f o r use i n connection with t h i s p r o j e c t . Two of the p l a t e s , one i n U and one i n B, were obtained at prime focus with the 4.0 meter t e l e s c o p e at the Cerro T o l o l o Inter-American Observatory (CTIO) by J . Hesser. The others are 3.6 meter p l a t e s c o n s i s t i n g of one B p l a t e and two V p l a t e s . These were ob t a i n e d with the Canada-France-Hawaii Telescope (CFHT) on Mauna Kea at prime focus by H. B. R i c h e r . Table I summarizes the r e l e v a n t i n f o r m a t i o n concerning the p l a t e m a t e r i a l . TABLE I: LIST OF PHOTOGRAPHIC PLATES PLATE NUMBER DATE TELESCOPE FILTER EMULSION EXPOSURE (min.) 4279 PF J u l y /79 CTIO UG-2 1 03aO 60 4277 PF J u l y /79 CTIO GG 385 1 03aO 20 A-51 3 June /80 CFHT GG 385 I l l a J 90 A-51 5 June /80 CFHT GG 495 IlaD 60 A-51 8 June /80 CFHT GG 495 Il a D 60 4 5 2.2 THE BLINK SURVEY The U and B CTIO 4.0 meter p l a t e s , being the best matched p a i r , were b l i n k e d using the U n i v e r s i t y of B r i t i s h Columbia Astronomy department's b l i n k comparator. The b l i n k survey was performed over the e n t i r e f i e l d and o b j e c t s deemed to be blue were noted f o r f u r t h e r study. I t was apparent r i g h t at the s t a r t that there were l a r g e numbers of extremely f a i n t blue o b j e c t s extending a l l the way to the edges of the f i e l d . Most of these were v i s i b l e only on the U p l a t e . T h i s i s probably due to the f a c t that the U and the B p l a t e s have l i m i t i n g magnitudes of 22.3 and 22.6, r e s p e c t i v e l y . T h e r e f o r e , blue o b j e c t s near the U p l a t e l i m i t would not be observed on the B p l a t e . A f t e r completion of the survey, the UV b r i g h t c a n didates were reexamined and were e l i m i n a t e d from the survey i f t h e i r q u a l i f i c a t i o n s ( i . e . U - B < 0 by v i s u a l i n s p e c t i o n ) as UV b r i g h t o b j e c t s were dubious. T h i s l e f t a t o t a l of 1096 blue o b j e c t s i n an annulus extending from 3.9' to 23.7' from the c l u s t e r c e n t e r . The region w i t h i n 3.9' of the c e n t e r was not e x t e n s i v e l y b l i n k e d f o r ca n d i d a t e s due to the extreme crowding e f f e c t s i n t h i s r e g i o n . However, the o u t l y i n g r e g i o n s f a r t h e r than 23.7' from the center were b l i n k e d , but p a r t s of t h i s area were not completely c l e a r of the edges of the p l a t e s and were consequently excluded i n the accumulation of the b l i n k s t a t i s t i c s . A second check of the o b j e c t s produced a l i s t of blue c a n d i d a t e s which were apparent on both the U and the B 6 p l a t e s . These o b j e c t s were c o n s i d e r e d to be the best candidates and were set a s i d e to be photometered. The number of o b j e c t s i n t h i s l i s t t o t a l l e d 74 and they are i n d i c a t e d on the f i n d i n g c h a r t s i n APPENDIX I I . Although s e v e r a l of these o b j e c t s are l o c a t e d i n the o u t l y i n g regions of the p l a t e , they are s u f f i c i e n t l y f a r away from the edges and were p e r m i t t e d to be candidates f o r photometry. The f a i n t e r blue c a n d i d a t e s were not photometered; s i n c e they appeared only on the U p l a t e , i t was decided that the U i n f o r m a t i o n alone would not be p a r t i c u l a r l y u s e f u l . 2.3 PHOTOGRAHIC PHOTOMETRY 2.3.1 PHOTOMETRIC STANDARDS The standards used to c a l i b r a t e the photographic photometry were obtained from a l i s t of s t a r s photometered using a CCD by Richer and Fahlman (1985). T h i r t y three s t a r s were s e l e c t e d from t h e i r "E" f i e l d and 36 were s e l e c t e d from t h e i r "F" f i e l d . These f i e l d s are 3' x 5' each and are l o c a t e d about 5' from the c l u s t e r c e n t e r . A l i s t of these standards i s given i n Table II along with t h e i r c o r r e s p o n d i n g magnitudes. Column 2 of the t a b l e d i s p l a y s Richer and Fahlman's d e s i g n a t i o n of these s t a r s . 7 TABLE I I : CCD STAR RF NO. U E FIELD 1 9001 18. 2 1 3 21 . 3 1 4 20. 4 225 19. 5 23 20. 6 27 18. 7 221 20. 8 437 19. 9 9018 18. 10 702 20. 1 1 470 18. 12 274 18. 1 3 275 19. 1 4 60 18. 1 5 86 18. 1 6 605 21 . 1 7 606 19. 18 599 19. 1 8A 9080 18. 19 550 20. 20 319 19. 21 124 19. 22 128 18. 23 493 20. STANDARDS B V 089 17.857 ' 17.100 255 20.810 20.041 944 20.355 19.267 042 18.779 17.928 941 20.345 19.262 423 18.263 17.424 586 20 . 112 19.038 666 19.371 18.434 332 18.154 17.304 176 19.863 18.858 1 07 18.900 18.021 820 18.870 18. 169 952 19.747 18.792 576 18.545 1 7 .776 377 18.389 17.628 016 20.558 19.346 370 19.291 18.395 1 67 19.014 18.058 076 1 7.969 17.121 624 20.313 19.244 296 19.255 18.355 077 18.964 18.061 1 93 18.161 17.341 228 20.163 19.209 8 TABLE II ( c o n t . ) : CCD STANDARDS STAR RF NO. U B V 24 308 20.842 20.391 19.278 25 112 20.320 19.993 18.941 26 12 23.055 22.575 21.217 27 220 - 22.836 20.950 28 441 22.910 22.257 20.964 29 273 - 23.383 21.639 30 704 21.993 21.771 20.574 31 600 22.038 21.477 20.180 32 569 24.804 23.376 21.501 F FIELD 1 127 18.202 18.113 17.277 2 126 21.543 21.423 20.457 3 117 20.839 20.320 19.199 4 80 18.632 18.494 17.630 5 2032 18.886 18.693 6 26 20.390 19.976 18.911 7 1002 21.253 8 22 21.556 21.155 19.898 9 23 18.368 18.218 17.446 10 9 18.795 18.648 17.793 11 42 20.210 19.031 19.130 12 201 21.130 20.953 20.029 13 200 17.887 17.754 16.949 14 3085 18.793 18.628 17.756 15 208 20.644 20.065 18.947 9 TABLE II ( c o n t . ) : CCD STANDARDS STAR RF NO. U B V 1 6 226 20.610 20.480 19.593 17 225 20.852 20.332 19.233 18 224 19.764 19.466 18.496 19 223 — — 17.457 20 245 21 .230 20.802 19.709 21 244 21 .506 21.300 20.472 22 254 20.830 19.950 19.123 23 395 19.529 19.269 18.309 24 362 19.879 19.593 18.587 25 381 18.983 18.775 17.899 26 384 18.054 17.898 17.095 27 532 20.100 19.614 18.546 28 517 20.237 19.833 18.824 29 438 21.184 20.562 19.444 30 83 23.356 22.092 20.469 31 34 23.933 23.271 22.648 32 28 24.276 23.546 21.584 33 7 23.860 23.462 22.274 34 202 — 22.752 20.721 38 227 22.884 21.793 20.347 39 417 23.469 23.105 21.480 2.3.2 THE PDS DATA The Photometric Data System (PDS) microdensitometer at the Dominion A s t r o p h y s i c a l Observatory was used to 10 d i g i t i z e the images of the candidates and standards t h a t were s e l e c t e d f o r photometry. The microdensitometer was set at a square a p e r t u r e of 22 microns per p i x e l and an a r r a y of 40 x 40 p i x e l s c e ntered about each candidate and standard was scanned. The c a n d i d a t e s and standards on each plate were scanned i n one continuous run without adjustments of any s o r t made on the microdensitometer to ensure photometric c o n s i s t e n c y between the standards and a l l of the c a n d i d a t e s . The microdensitometer was turned on f o r at l e a s t a f u l l two hours before each run to allow s u f f i c i e n t time f o r i t to s t a b i l i z e . I t should be noted that the X-Y c o o r d i n a t e s of the a r r a y c e n t e r s were i n i t i a l l y entered i n t o the PDS machine using the o b j e c t s on the 4.0 meter U p l a t e f o r r e f e r e n c e . These p o s i t i o n s were s t o r e d and were l a t e r used again f o r automated l o c a t i o n of the photometric c a n d i d a t e s and standards on the 4.0 meter B p l a t e . As expected, f i e l d d i s t o r t i o n s of the B p l a t e r e l a t i v e to the U p l a t e were minimal. Indeed, a l l the images of the o b j e c t s on the B p l a t e were l o c a t e d w e l l w i t h i n the r a s t e r boundaries and most were near the a r r a y c e n t e r s . However, s i n c e the 3.6 meter p l a t e s had d i f f e r e n t p l a t e s c a l e s , the p o s i t i o n data obtained from the 4.0 meter U p l a t e c o u l d not be used d i r e c t l y as input f o r an automated scan of the 3.6 meter p l a t e s . I t would seem that a s c a l i n g f a c t o r a p p l i e d to the 4.0 meter p o s i t i o n data may provide the necessary c o r r e c t i o n ; however, i t 11 was soon r e a l i z e d that the r e l a t i v e f i e l d d i s t o r t i o n s from the CTIO p l a t e s to the CFHT p l a t e s were q u i t e l a r g e (on the order of 300 microns compared to the 880 x 880 micron a r r a y s ) . In f a c t , the d i f f e r e n c e s were enough to cause some images to be so p o o r l y a l i g n e d , that p a r t s of those images were t r u n c a t e d at the edges of the frames. In the end, the p o s i t i o n s had to be re e n t e r e d using the 3.6 meter B p l a t e as r e f e r e n c e ( s i n c e t h i s was the deepest 3.6 meter p l a t e ) . The other CFHT p l a t e s were scanned using these p o s i t i o n s . F i e l d d i s t o r t i o n was minor among the CFHT p l a t e s and the scans produced s a t i s f a c t o r i l y centered images. 2.4 REDUCTIONS The d i g i t i z e d frames were reduced using the two dimensional image p r o c e s s i n g program SUPERTOODEE i n i t i a l l y developed by G. G. Fahlman ( N i c o l 1984). T h i s program s u p p l i e s a command language f a c i l i t y which can be used to implement a v a i l a b l e image p r o c e s s i n g r o u t i n e s and packages. Simple programs and macros can be designed to t a i l o r the r o u t i n e s to the user's own needs. The f o l l o w i n g are d e s c r i p t i o n s of the two techniques employed using SUPERTOODEE to reduce the PDS data. 2.4.1 APERTURE PHOTOMETRY The f i r s t method simulates the procedure of ape r t u r e photometry. Since most of the frames of the M4 1 2 candidates and standards c o n t a i n e d a s i n g l e o b j e c t near the center of the a r r a y , a crude p o s i t i o n of the o b j e c t image was f i r s t determined by l o c a t i n g the maximum i n t e n s i t y p i x e l i n a 10 x 10 subframe about the a r r a y c e n t e r . The subframe was searched i n order to screen out any o b j e c t s at the p e r i p h e r y , should they e x i s t , i n the event that they may be confused with the o b j e c t of i n t e r e s t . T h i s technique worked w e l l except f o r some frames c o n t a i n i n g very f a i n t images. In these frames, nois e peaks or bad p i x e l s with i n t e n s i t i e s g r e a t e r than the maximum i n t e n s i t i e s of the o b j e c t were l o c a t e d i n s t e a d . A second run using a more a p p r o p r i a t e subframe was necessary i n these cases. Once the crude center was l o c a t e d , a refinement of the o b j e c t p o s i t i o n was determined by performing a l e a s t squares f i t of a c i r c u l a r l y symmetric Gaussian to the p i x e l s w i t h i n a 3 - p i x e l r a d i u s of the crude o b j e c t c e n t e r . A c i r c u l a r a p e r t u r e with a diameter of 8 p i x e l s was then p o s i t i o n e d at t h i s center and the i n t e n s i t i e s of a l l the p i x e l s w i t h i n the ape r t u r e were summed to simulate aperture photometry. Throughout the r e d u c t i o n , d i s t a n c e s and p o s i t i o n s i n the d i g i t i z e d frames, except the crude o b j e c t c e n t e r s , were manipulated with r e s o l u t i o n s to f r a c t i o n s of a p i x e l i n order to enhance accuracy. However, the number of square integral p i x e l s e n c l o s e d by a c i r c u l a r a p e r t u r e i s dependent upon the p o s i t i o n of the ap e r t u r e 1 3 c e n t e r . For example, the number of i n t e g r a l p i x e l s i n c l u d e d w i t h i n a f i x e d c i r c u l a r a p e r t u r e p o s i t i o n e d near the center of a given p i x e l i s d i f f e r e n t from the number that would be encl o s e d i f the ape r t u r e center was near one of the p i x e l ' s c o r n e r s . The d i f f e r e n c e from one po i n t to another can produce v a r i a t i o n s as l a r g e as 4 or 5 i n the t o t a l number of p i x e l s (about 50 f o r an 8 - p i x e l diameter a p e r t u r e ) . These number f l u c t u a t i o n s were reduced to t y p i c a l l y l e s s than one p i x e l by s p l i t t i n g the p i x e l s at the edges of the ap e r t u r e i n t o q u a r t e r - p i x e l s (each c o n t a i n i n g a qu a r t e r of the o r i g i n a l p i x e l ' s f l u x ) and i n c l u d i n g the ones which l i e w i t h i n the a p e r t u r e . The -next step was to s u b t r a c t out the sky c o n t r i b u t i o n to the i n t e g r a t e d aperture f l u x . The sky i n each frame was estimated independently by examining the p i x e l s i n an annulus around the obj e c t image extending from 10 p i x e l s out to 14 p i x e l s from the image c e n t e r . The p i x e l s i n the annulus with i n t e n s i t i e s g r e a t e r than the mean i n t e n s i t y of a l l the p i x e l s i n the frame were r e j e c t e d i n order to reduce the l i k e l i h o o d of contamination due to p e r i p h e r a l s t a r images t h a t may be p a r t i a l l y i n c l u d e d i n the s e l e c t e d annulus. The mean, mode, and median were c a l c u l a t e d f o r the remaining p i x e l s of the annulus and were used to determine the "pseudomode" (3 • MEDIAN - 2 • MEAN) and i t s standard d e v i a t i o n . The p i x e l s were then s o r t e d — any p i x e l which 1 4 had i n t e n s i t i e s more than 3 sigma away from the pseudomode were r e j e c t e d . A new pseudomode was c a l c u l a t e d and the process i t e r a t e d u n t i l no f u r t h e r p i x e l s were r e j e c t e d . The f i n a l pseudomode was then adopted as the best estimate f o r a t y p i c a l sky p i x e l of the frame. The sky p i x e l estimate was m u l t i p l i e d by the number of p i x e l s c o n t a i n e d w i t h i n the a p e r t u r e and was s u b t r a c t e d from the i n t e g r a t e d f l u x to o b t a i n the d e s i r e d aperture f l u x f o r the o b j e c t . C a l i b r a t i o n of the a p e r t u r e f l u x with standard UBV magnitudes w i l l be d i s c u s s e d in s e c t i o n 2.5. 2.4.2 PHOTOMETRY BY STELLAR PROFILE FITTING A second method was a l s o e x p l o r e d i n the hopes of p r o v i d i n g more a c c u r a t e photometry. The method e n t a i l s f i t t i n g a s t e l l a r p r o f i l e to the o b j e c t image. The amount of s c a l i n g r e q u i r e d to o b t a i n the best f i t c o n t a i n s the r e l e v a n t photometric i n f o r m a t i o n that can r e a d i l y be converted i n t o a magnitude. A s u i t a b l e s t e l l a r p r o f i l e was o b t a i n e d by t a k i n g the average of the images from 5 of the photometric standards. These images were c a r e f u l l y examined to ensure that a l l were reasonably b r i g h t (peak s i g n a l - t o - n o i s e r a t i o s at l e a s t 10:1), w e l l centered, unsaturated, and uncontaminated ( i . e . t here were no other s t a r s i n the frame besides the s t a n d a r d ) . 1 5 A cub i c b i - s p l i n e f u n c t i o n was f i t t e d to the averaged s t e l l a r p r o f i l e to give a s e m i - e m p i r i c a l l y determined p o i n t spread f u n c t i o n (PSF). For each of the d i g i t i z e d frames, a 12 x 12 p i x e l subframe was e x t r a c t e d and p i x e l s w i t h i n a 6 - p i x e l r a d i u s of the PSF were used to f i t the image i n t h i s subframe. The f i t t i n g r o u t i n e i t e r a t e d to a maximum of 3 times, or u n t i l a 2.6 sigma f i t was obtained. T h i s method r e q u i r e d only an approximate i n i t i a l estimate of the sky, s i n c e the sky background l e v e l was a l s o determined by the f i t t i n g . The 5 x 5 p i x e l subframes at each of the 4 c o r n e r s of the frame were then i s o l a t e d and the mode of the p i x e l s i n these subframes was found. The mode s u f f i c e d as the i n i t i a l sky estimate. The s c a l i n g r a t i o r e q u i r e d to s c a l e the PSF to f i t the ob j e c t image c o u l d thus be c a l c u l a t e d . 2.5 CALIBRATION Since the ape r t u r e f l u x e s and the s c a l i n g r a t i o s of the standard s t a r s on each p l a t e are i n themselves, s e t s of i n t e r n a l l y c o n s i s t e n t magnitudes, they need only be c a l i b r a t e d to the UBV system i n order to y i e l d the d e s i r e d photometry. T h i s was done by t a k i n g the common l o g a r i t h m of the a p e r t u r e f l u x e s or s c a l i n g r a t i o s of the standards on each p l a t e and p l o t t i n g them up a g a i n s t t h e i r corresponding magnitudes. The curve obtained c a l i b r a t e s a p e r t u r e f l u x e s or s c a l i n g r a t i o s with the a p p r o p r i a t e magnitudes f o r each 1 6 p l a t e . It i s from these c a l i b r a t i o n curves that the q u a l i t y of the p l a t e used for photometry c o u l d be p r o p e r l y assessed. The V p l a t e A-518, f o r i n s t a n c e , c o n t a i n e d images which were s l i g h t l y extended due to an emergency stop on the CFHT te l e s c o p e run when t h i s p l a t e was exposed. I t was not expected that aperture photometry would work w e l l on t h i s p l a t e and the s c a t t e r of the p o i n t s and the shape of the curve confirmed t h i s p r e d i c t i o n . I t was hoped, however, that the PSF f i t t i n g method would succeed s i n c e the i n t r i n s i c shape of the PSF i s i r r e l e v a n t as long as i t i s s i m i l a r to the p r o f i l e s of the o b j e c t images on the p l a t e . U n f o r t u n a t e l y , the method d i d not g i v e the d e s i r e d r e s u l t s . Tt may be that small r e l a t i v e r o t a t i o n s i n the o b j e c t o r i e n t a t i o n dependant upon the o b j e c t p l a t e p o s i t i o n were present, reducing the e f f e c t i v e n e s s of t h i s technique when n o n - c i r c u l a r l y symmetric PSF's are used. I t was decided that the data f o r t h i s p l a t e should be d i s c a r d e d from the photometry. The CTIO B p l a t e , although by i n s p e c t i o n appeared to be a good p l a t e , the c a l i b r a t i o n curves obtained f o r i t showed a l a r g e amount of s c a t t e r . The reason i n t h i s case was not c l e a r . The curves c o u l d be r e s o l v e d i n t o two rough sequences, approximately 0.2 magnitudes a p a r t , each sequence co r r e s p o n d i n g to e i t h e r the E f i e l d or the F f i e l d s tandards. T h i s would seem to i n d i c a t e an asymmetry i n the magnitudes of the standards between the E and the F f i e l d ; 17 however, t h i s was not observed with the CFHT B p l a t e . A p o s s i b l e e x p l a n a t i o n may be that a g r a d i e n t e x i s t s over the CTIO p l a t e but i t i s not known how t h i s c o u l d have o c c u r r e d . In any event, i t was concluded that only the b r i g h t e r s t a r s (B < 20) c o u l d be photometered on t h i s p l a t e with a c c u r a c i e s comparable to that of the other p l a t e s . Since p r a c t i c a l l y a l l of the QSO and white dwarf candidates were f a i n t e r than t h i s l i m i t , the p l a t e was not used f o r photometric purposes. T h i s l e f t o nly the CTIO U p l a t e , the CFHT B p l a t e , and the remaining CFHT V p l a t e f o r photometry. These p l a t e s produced q u i t e reasonable c a l i b r a t i o n curves and are shown in F i g u r e s 1 — 6. The s o l i d l i n e s are the simplest b e s t - f i t p olynomials to the p o i n t s . The degrees of the polynomials are l i s t e d i n column 3 of Table I I I along with the number of standards used i n each c a l i b r a t i o n (column 4) and the standard d e v i a t i o n f o r each f i t (column 5). It can be seen, by comparing the aperture f l u x c a l i b r a t i o n curves to the s c a l i n g r a t i o c a l i b r a t i o n curves f o r the same p l a t e s , that the method of aperture photometry seemed to produce the best r e s u l t s . T h i s i s s u r p r i s i n g s i n c e i t would seem that s t e l l a r p r o f i l e f i t t i n g should prove to be a more r i g o r o u s technique. I t should be noted, however, th a t p r o f i l e f i t t i n g methods do indeed produce b e t t e r r e s u l t s with s a t u r a t e d images. By i g n o r i n g the s a t u r a t e d c e n t r a l p i x e l s , the PSF can be f i t t e d to the outer non-saturated p i x e l s of the image. There i s no such compensation f o r s a t u r a t i o n e f f e c t s i n aperture photometry. 30 l i i i i I 17.0 18.0 19.0 20.0 21.0 22.0 U MAGNITUDE FIGURE 1: U P l a t e Flux C a l i b r a t i o n Curve. The standard CCD U magnitudes are p l o t t e d a g a i n s t t h e i r c o r r e s p o n d i n g a p e r t u r e f l u x e s ( i n t e r n a l f l u x u n i t s ) . The s o l i d curve i s the best f i t to the data. 19 4.4 I 1 r 2 4 I i i i i i l 18.0 19.0 20.0 21.0 22.0 23.0 24.0 B MAGNITUDE FIGURE 2: B P l a t e F l u x C a l i b r a t i o n Curve. The standard CCD B magnitudes are p l o t t e d a g a i n s t t h e i r c o rresponding aperture f l u x e s ( i n t e r n a l f l u x u n i t s ) . The s o l i d curve i s the best f i t to the data. 20 4.2 4.0 3.8 x cc 3.6 cc Q_ CJ3 Q 3.4 3.2 3.0 2.8 — 1 1 1 -+\ 1 — — — — 1 1 1 1 17.0 18.0 19.0 20.0 V MAGNITUDE 21.0 22.0 FIGURE 3: V P l a t e Flux C a l i b r a t i o n Curve. The standard CCD V magnitudes are p l o t t e d a g a i n s t t h e i r corresponding aperture f l u x e s ( i n t e r n a l f l u x u n i t s ) . The s o l i d curve i s the best f i t to the data. 21 0.2 i f 1 1 1 1 -\2 1 1 1 i I 18.0 19.0 20.0 21.0 22.0 U MAGNITUDE FIGURE 4: U P l a t e R a t i o C a l i b r a t i o n Curve. The standard CCD U magnitudes are p l o t t e d a g a i n s t t h e i r c o r r e s p o n d i n g PSF s c a l i n g r a t i o s . The s o l i d curve i s the best f i t to the data. 22 I I I I I 1 1 I 17.0 18.0 19.0 20.0 21.0 22.0 23.0 24.0 B MAGNITUDE FIGURE 5: B P l a t e R a t i o C a l i b r a t i o n Curve. The s t a n d a r d CCD B magnitudes a r e p l o t t e d a g a i n s t t h e i r c o r r e s p o n d i n g PSF s c a l i n g r a t i o s . The s o l i d c u r v e i s the b e s t f i t t o the d a t a . 23 0.3 -1.1 i . . 1 . 1 16.5 17.5 18.5 19.5 20.5 21.5 V MAGNITUDE FIGURE 6: V P l a t e R a t i o C a l i b r a t i o n Curve. The standard CCD V magnitudes are p l o t t e d a g a i n s t t h e i r c o rresponding PSF s c a l i n g r a t i o s . The s o l i d curve i s the best f i t to the data. 24 TABLE I I I : STATISTICS OF CALIBRATION CURVES PLATE CALIBRATION DEGREE STANDARDS SIGMA 4279 PF (U) Flux 1 41 0.09 A-513 (B) Flux 2 48 0.11 A-515 (V) Flux 2 46 0.12 4279 PF (U) Ra t i o 3 41 0.16 A-513 (B) Ratio 2 58 0.16 A-515 (V) Ratio 2 53 0.15 Because of t h i s , s a t u r a t e d images have been excluded from the a p e r t u r e f l u x c a l i b r a t i o n . At the f a i n t end of the c a l i b r a t i o n curves, i t can be seen that the method of aper t u r e photometry performs at l e a s t as w e l l as the p r o f i l e f i t t i n g method. The o v e r a l l s c a t t e r of the p l o t s a l s o appear to be s m a l l e r on the ape r t u r e f l u x c a l i b r a t i o n c urves. On the b a s i s of t h i s comparison, i t was decided to adopt aperture photometry i n reducing the remaining candidate images. 2.6 COLOUR TERMS A f t e r f i n d i n g i n s t r u m e n t a l magnitudes f o r the ca n d i d a t e s , the conversi o n to the standard UBV system was undertaken using the f o l l o w i n g t r a n s f o r m a t i o n s : U - B = i / / ( u - b ) + S u b , (1 ) B - V = < M b - v ) + $ b v , (2) V - v = M ( B - V ) + $ v. (3) 25 The c o e f f i c i e n t s in the above equations were determined from the standard s t a r s and are l i s t e d i n Table IV. TABLE IV: COLOUR TRANSFORMATION COEFFICIENTS M *v * $bv * $ub 0.06 -0.06 1.00 0.01 0.89 0.02 The d i f f e r e n c e between the in s t r u m e n t a l c o l o u r s and the transformed c o l o u r s are not l a r g e , t y p i c a l l y a few hundreths of a magnitude, which i s g e n e r a l l y smaller than the t y p i c a l e r r o r s i n the photometry. 2.7 RESULTS OF THE PHOTOMETRY The photometered ca n d i d a t e s are t a b u l a t e d in Table V, which l i s t s t h e i r b l i n k survey d e s i g n a t i o n s i n column 1. T h e i r observed V magnitudes and observed B-V and U-B c o l o u r s are shown i n the succeeding 3 columns. S e v e r a l of the cand i d a t e s were too f a i n t i n V to be photometered. For these, a b r i g h t l i m i t of V ^ 22 has been assumed and d i s p l a y e d i n the t a b l e along with the cor r e s p o n d i n g upper l i m i t s f o r B-V. Column 5 e i t h e r shows the c l a s s i f i c a t i o n of the o b j e c t s based on t h e i r p o s i t i o n s on the c o l o u r - c o l o u r diagram (see Chapters 3 and 4), or c o n t a i n s a comment to the e f f e c t that the image i s n o n s t e l l a r . The i n f o r m a t i o n on the image s t r u c t u r e was obtained by using the U n i v e r s i t y of B r i t i s h Columbia Astronomy department's I 2 S Image D i s p l a y System to examine a l l of the photometered candidates 26 i n t e r a c t i v e l y f o r any e x t e n s i o n s i n the images. O b j e c t number 1377 appeared t o be extended on the V p l a t e and i t i s the s o l e o b j e c t photometered t h a t might be c o n s i d e r e d to be a c a n d i d a t e f o r a double image; the w e i g h t i n g f o r such a c l a i m , however, i s not h i g h . 27 TABLE V: PHOTOMETRIC WD AND QSO CANDIDATES IN M4 OBJECT V B-V U-B COMMENTS 86 18.45 0.88 -0.04 sdG 90 20.41 0.23 -1 .06 WD 98 <22 <0 . 4 -0.85 1 04 <22 <0.8 -1 .67 340 21.14 0.89 -0.37 QSO 407 21 .06 0.71 -0.18 sdG 475 20.82 1 .07 -0.47 QSO 494 21 .02 0.85 -0.67 n o n s t e l l a r 497 21.61 0.84 -1 .43 n o n s t e l l a r 591 20. 1 6 1 .04 -0.21 QSO 595 20.34 1.14 -0.46 QSO 601 20.42 1 .68 -0.32 QSO 604 20.93 0.86 -0.36 QSO 644 20.49 0.32 -1.13 WD 653 18.36 0.92 0.11 SdG 659 20.81 1.14 -0.46 QSO 671 20.23 1.16 -0.30 QSO 675 21.75 0.70 -0.18 sdG 687 21 .27 1 .24 -0.69 QSO 695 20.69 1 .24 -0.41 QSO 696 21.18 1.17 -0.82 QSO 699 20.30 0.95 -0.29 QSO 702 21 .33 0.56 -0.95 QSO 710 19.86 0.24 -0.62 WD 716 20.60 1 .24 -0.05 SdG 28 TABLE V ( c o n t . ) : PHOTOMETRIC WD AND QSO CANDIDATES IN M4 OBJECT V B-V U-B COMMENTS 724 20.73 0.92 0.02 sdG 731 20.33 1 .39 -0.31 QSO 748 20.72 1 .23 -0.54 QSO 770 1 9.75 0.85 -0.30 QSO 772 19.83 1 .07 -0.33 QSO 774 19.04 0.12 -0.51 WD 810 20.52 1.18 -0.62 QSO 831 20.33 0.12 -1 .09 WD 853 20.63 1 .20 -0.56 QSO 870 20.94 1 .00 -1.16 QSO 936 20.49 0.85 -1 .04 QSO 942 20.65 1 .02 -0.58 QSO 957 20.47 1 .02 -0.36 QSO 973 20.20 1.21 -0.22 QSO 974 20.85 1 .48 -0.42 QSO 981 19.36 1.11 0.06 sdG 988 22.24 0.44 -0.49 WD 1 009 21.02 0.71 -0.63 QSO 1 020 20.80 1 .09 -0.35 QSO 1 042 20.08 1 .22 -0 . 26 QSO 1 082 21 .00 1 .28 -0.40 QSO 1 1 38 20.45 1.21 -0.07 sdG 1 1 44 21.19 1 .30 -0.54 QSO 1 1 57 21.13 1 .02 0.04 sdG 1 187 <22 <0.7 -1 .52 29 TABLE V ( c o n t . ) : PHOTOMETRIC WD AND QSO CANDIDATES IN M4 OBJECT V B-V U-B COMMENTS 1218 21 .57 1 .39 -0.70 QSO 1 221 20.99 1 .42 -0.65 QSO 1 223 20.86 0.35 -1.15 WD 1 231 21 .33 0.70 -0.06 SdG 1 254 21 .35 1 .33 -1.13 n o n s t e l l a r 1285 19.18 0.36 -0.59 WD 1 297 20.95 0.96 - 0 . 1 9 QSO 1305 21.76 0.19 -0.62 WD 1314 20.50 0.80 -0.55 QSO 1 320 1 9.22 0.92 -0.12 n o n s t e l l a r 1 336 21 .08 0.02 -1.11 WD 1 362 21.07 0.76 -0.88 QSO 1 377 21.10 1 .35 -0.84 double? 1 392 <22 <0.8 -1.41 1 461 1 9.34 1 . 04 -0.04 SdG 1 472 21 .32 1 . 34 -1 .32 n o n s t e l l a r 1 479 21 .05 1.12 -0.92 QSO 1 567 21.83 0.39 -1 .26 WD 1 647 21 .23 0.97 -0.74 QSO 1659 <22 <0.4 -1.16 1 699 21 .87 0.30 -0.69 WD 1710 18.91 0.87 -0.70 n o n s t e l l a r 1747 <22 <0.4 -0.81 C252 <22 <0.5 -1 .04 Chapter 3 WHITE DWARFS IN M4 3.1 RESULTS OF THE BLINK SURVEY In order to see i f a r a d i a l number g r a d i e n t e x i s t s i n the d i s t r i b u t i o n of the blue o b j e c t s , the f i e l d was d i v i d e d up i n t o 10 c o n c e n t r i c a n n u l i and a l l blue o b j e c t s surveyed w i t h i n each were counted. Table VI g i v e s the t o t a l s of the object counts f o r each annulus. TABLE VI: BLUE OBJECT RADIAL DISTRIBUTION ABOUT M4 ANNULUS OBJECTS LOG R LOG F (arc min.) COUNTED 3.9-6.0 79 0.71 0.07 6.0-7.9 93 0.85 0.06 7.9-9.8 90 0.95 -0.07 9.8-11 .9 1 18 1 .04 -0.09 11.9-13.9 101 1.11 -0.19 13.9-15.9 108 1.17 -0.24 15.9-17.7 1 1 6 1 .23 -0.22 17.7-19.8 1 19 1 .27 -0.31 19.8-21.7 1 29 1 .32 -0.29 21.7-23.7 1 43 1 .36 -0.31 The t h i r d column shows the l o g a r i t h m of the e f f e c t i v e r a d i u s R of the annulus ( i . e . the r a d i u s b i s e c t i n g the area of the annulus) and the l a s t column g i v e s the l o g a r i t h m of the frequency F of blue o b j e c t s per square minute of arc i n the 30 31 annulus. F i g u r e 7 i s a p l o t of l o g R a g a i n s t l o g F r e v e a l i n g a very n o t i c e a b l e i n c r e a s e i n the c o n c e n t r a t i o n of blue o b j e c t s towards the center of the c l u s t e r . It should be po i n t e d out, however, that the c o n t r i b u t i o n to the number of blue o b j e c t s by foreground white dwarfs, QSOs, hot f i e l d subdwarfs, and f a i n t blue g a l a x i e s must be c o n s i d e r e d before an attempt i s made to estimate the number of c l u s t e r white dwarfs. In f a c t , the foreground number of white dwarfs expected to be observed i n the M4 f i e l d can be a s c e r t a i n e d using Green's (1980) l u m i n o s i t y f u n c t i o n f o r s o l a r neighborhood white dwarfs. Under h i s assumption of f l a t d i s k model d i s t r i b u t i o n s to v a r i o u s s c a l e h e i g h t s dependent upon the i n t r i n s i c l u m i n o s i t i e s of the white dwarfs, an estimate of the number of g a l a c t i c foreground white dwarfs can be made by i n t e g r a t i n g the space d e n s i t i e s in the cones out to M4. Of course, the r e s t r i c t i o n s on the extent of the cones due to the t h i c k n e s s e s of the d i s k s and the l i m i t i n g magnitude of the survey must be taken i n t o c o n s i d e r a t i o n . Since the l i m i t i n g magnitude of the survey i n U i s 22.3, a t y p i c a l white dwarf candidate at the p l a t e l i m i t would have V -23.5. A c a l c u l a t i o n to t h i s l i m i t i n V g i v e s a r e s u l t of about 80 expected foreground white dwarfs i n the f i e l d ( i . e . 0.04 / sq. min.) — the d e t a i l s of which can be found i n APPENDIX I. T h i s estimate i s approximately twice that found from Kron's (1980) counts of s t a r s b l u e r than (B-V) 0 0.25 ( a c t u a l l y , ( J - F ) 0 = 0.25) down to V 0 = 22.5 ( a c t u a l l y , 32 CD O FIGURE 7: R a d i a l Blue Object D i s t i b u t i o n . R i s the e f f e c t i v e r a d i u s of the annulus i n arc min. from the c l u s t e r c e n t e r and F i s the number of o b j e c t s per square minute of arc i n the annulus. 33 ( j + F ) 0 / 2 = 22.45) i n the f i e l d s of SA 57 and SA 68. However, these f i e l d s have g a l a c t i c l a t i t u d e s of b 86° and b 46°, r e s p e c t i v e l y , as opposed to the low l a t i t u d e of M4 (b -16°). T h e r e f o r e , i t i s not s u r p r i s i n g that they may c o n t a i n fewer foreground white dwarfs. From F i g u r e 7, the l a s t t hree p o i n t s d e p i c t i n g the f u r t h e s t a n n u l i from the c l u s t e r c e n t e r do not appear to show much g r a d i e n t i n F. I t i s assumed that these p o i n t s are i n d i c a t i v e of the background c o n t r i b u t i o n . Since these p o i n t s g i v e a value of about 0.5 o b j e c t s per square minute of a r c , they w e l l outnumber the estimated white dwarf foreground and are most l i k e l y composed of e x t r a g a l a c t i c o b j e c t s and h a l o subdwarfs. A f t e r s u b t r a c t i o n of t h i s assumed background from the numbers i n the other a n n u l i , the c o r r e c t e d count d i s t r i b u t i o n can be found and i s t a b u l a t e d i n Table V I I . TABLE V I I : BACKGROUND CORRECTED BLUE OBJECT DISTRIBUTIONS ANNULUS(arc min.) LOG R LOG F 3.9-6.0 0.71 -0.17 6.0-7.9 0.85 -0.19 7.9-9.8 0.95 -0.45 9.8-11.9 1 . 04 -0.50 11.9-13.9 1.11 -0.84 13.9-15.9 1.17 -1.12 15.9-17.7 1 .23 -0.99 F i g u r e 8 i s a p l o t of the r e s u l t s d i s p l a y e d i n Table VII 34 0.07 -0.13 -0.33 -0.53 -0.73 -0.93 -1.13 --1.33 • i 1 1 r • A i r A • A • A A A • Legend • BLUE OBJECTS IN DIR. OF M4 A KING etal. M4 STAR COUNTS A • A 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 LOG R 1.4 1.2 1.0 0.8 £ t o L i -CU 0.6 3 0.4 H 0.2 0.0 1.4 FIGURE 8: R a d i a l Star and C o r r e c t e d Object D i s t r i b u t i o n s . R i s the same as i n F i g u r e 8, F (candidates) has been c o r r e c t e d f o r background, and F ( s t a r s ) i s f o r a l l s t a r s i n M4 (King et a l . 1968). 35 along with King et a l . ' s (1968) background c o r r e c t e d s t a r counts i n M4. Since we are d e a l i n g with only a component of the s t e l l a r p o p u l a t i o n i n M4, the d i f f e r e n c e in F at each R between King et a l . ' s data and the blue o b j e c t d i s t r i b u t i o n i s , of course, expected. However, the important c h a r a c t e r i s t i c of the two se t s of data i s that they both appear to reflect a similar gradient in the radial distribution. T h i s would tend to favor the view that the c o n c e n t r a t i o n of blue o b j e c t s i s a s s o c i a t e d with the c l u s t e r . T h e r e f o r e , i t i s a s s e r t e d that t h i s excess i n the number of blue o b j e c t s belong to the hot white dwarf p o p u l a t i o n of M4. The t o t a l number of white dwarfs i n the r e g i o n surveyed b r i g h t e r than U = 22 . 3 ( i . e. V - 23.5) i s then the t o t a l number of o b j e c t s (705) i n the f i r s t 7 a n n u l i minus the p r o j e c t e d background (468) i n t h i s region of 0.5 o b j e c t s per square minute of a r c . T h e r e f o r e , a t o t a l of 237 c l u s t e r white dwarfs are estimated to e x i s t i n M4 b r i g h t e r than M^ , =* 11 between 3.9' and 17.7' from the c l u s t e r c e n t e r . 3.2 PHOTOMETRIC WHITE DWARF CANDIDATES The candidates photometered and l i s t e d i n Table V are p l o t t e d on Fig u r e 9 i n the (U-B) 0 and (B-V) 0 c o l o u r - c o l o u r plane along with the f i d u c i a l Hyades main sequence and the blackbody l i n e (Matthews and Sandage 1963). The c o l o u r s have been dereddened using the c o l o u r excesses, E(B-V) = 0.37 (Richer and Fahlman 1984), and E(U-B) = [0.72 + 0.05 E(B-V)] 36 -1.6 -1.4 -1.2 -1.0 -0.8 -0.6 0.4 0.2 0.0 A A A A* o A o o o o o Legend O QSO A HOT WD V WD 0 sdG HYADES BB LINE O ° O L o o ° 0 < } \ 0 % \ o -0.4 0.0 0.4 0.8 1.2 1.6 (B-V) 0 FIGURE 9: Colour-Colour Diagram f o r Photometered Candidates. The f o l l o w i n g o b j e c t s are i n d i c a t e d : (1) WDs ( i n v e r t e d t r i a n g l e s ) ; (2) hot WDs ( t r i a n g l e s ) ; (3) QSOs ( c i r c l e s ) ; and (4) G subdwarfs (diamonds). The blackbody l i n e (dashed) and the Hyades f i d u c i a l ( s o l i d curve) are a l s o shown. 37 E(B-V). The candidates with n o n s t e l l a r images or assumed b r i g h t l i m i t s i n V are not shown. Six of the candidates have c o l o u r s t y p i c a l of white dwarfs and are p l o t t e d as i n v e r t e d t r i a n g l e s on the diagram. Another 6 o b j e c t s , blue i n B-V, have very blue c o l o u r s i n U-B and are i n d i c a t e d by the t r i a n g l e s . These may be extremely hot and t h e r e f o r e r e c e n t l y formed white dwarfs, or they may be p e c u l i a r emission l i n e o b j e c t s . T h e r e f o r e , a t o t a l of 12 p o s s i b l e white dwarfs have been found from the sample s e l e c t e d out f o r photometry. Assuming f o r the moment that these candidates are t r u l y white dwarfs, then the q u e s t i o n of c l u s t e r membership must be c o n s i d e r e d . From the a v a i l a b l e data, membership cannot be determined u n e q u i v o c a l l y ; however, the p o s i t i o n of the c a n d i d a t e s on the colour-magnitude diagram can be h i g h l y s u g g e s t i v e . F i g u r e 10 i n d i c a t e s that the 9 f a i n t e s t c a n d i d a t e s have B-V c o l o u r s and V magnitudes c o n s i s t e n t with the s u p p o s i t i o n that they are indeed hot c l u s t e r white dwarfs. They g e n e r a l l y f a l l i n the v i c i n i t y of the 0.51 M Q t h e o r e t i c a l c o o l i n g sequence f o r white dwarfs (transformed to the (V, B-V) plane from Sweeney's (1976) c o o l i n g curve using Shipman's (1972, 1979) temperature s c a l e s and b o l o m e t r i c c o r r e c t i o n r e l a t i o n s ) . C l u s t e r membership f o r these would imply that there are 5 white dwarfs with < 8.5. The other 4 p o s s i b l e members are somewhat f a i n t e r and undoubtedly represent a h i g h l y incomplete sampling of the white dwarfs with 8.5 < M^ . < 9.5, s i n c e the l i m i t i n g magnitude of the photometered candidates i n V i s 21. The 3 8 16.0 17.0 18.0 19.0 20.0 21.0 22.0 23.0 V . V V A A A A 24.0 -0.2 i A \ \ \ V I V A \ \ \ \ \ \ \ \ _ J L \ _ Legend M4 FIDUCIAL 0.51 M^WD V WD A HOT WD 0.0 0.2 0.4 0.6 0.8 1.0 1.2 B - V 1.4 1.6 FIGURE 10: Colour-Magnitude Diagram of M4. The M4 f i d u c i a l of Rich e r and Fahlman (1984) i s shown by the s o l i d l i n e . The 12 WD candidates are p l o t t e d with the same symbols as i n F i g u r e 9 and the dashed l i n e i s (1976). the 0.51 M, © c o o l i n g curve from Sweeney 39 remaining 3 candidates i n F i g u r e 10 appear to be too b r i g h t to be c o n s i d e r e d as c l u s t e r members and are assumed to be the observable foreground white dwarf component to V = 21 (V 0 20, assuming A v = 3 E ( B - V ) ) . The p r e d i c t e d number of foreground white dwarfs can once again be found f o r t h i s l i m i t from Green's survey (see APPENDIX I ) . The c a l c u l a t i o n g i v e s an estimate of approximately 8. From an o b s e r v a t i o n a l s t a n d p o i n t , Romanishin and Angel's (1980) b l i n k survey of comparison f i e l d s f o r t h e i r work on white dwarfs i n open c l u s t e r s g i v e s an average of about 6 per square degree ( i . e . about 3 per M4 f i e l d ) down to V 0 ~ 20. These f i e l d s are low in l a t i t u d e but the l i m i t i n g magnitudes are only approximate as they l a c k e d a c c u r a t e photometry. Taken a l t o g e t h e r , these numbers are not i n disagreement with the 3 o b j e c t s -detected i n the M4 f i e l d as foreground on the b a s i s of t h e i r c o l o u r s and magnitudes. T h e r e f o r e , a t o t a l of 9 o b j e c t s appear to be good candidates f o r hot, young, c l u s t e r white dwarfs. Notice should a l s o be given to 4 of the photometered candidates with a s s i g n e d b r i g h t l i m i t s i n V. In p a r t i c u l a r , o b j e c t s 98, 1659, and 1747, have V < 22 and (B-V) < 0.4. Object C252 has V < 22 and (B-V) < 0.5. A l l 4 candidates have U-B c o l o u r s of about -1. Without a more d e f i n i t e V magnitude, however, the i d e n t i f i c a t i o n of these candidates as white dwarfs at the c l u s t e r d i s t a n c e cannot be made with c e r t a i n t y . 40 3.3 DISCUSSION OF THE RESULTS Having found approximately 240 p o s s i b l e white dwarfs b r i g h t e r than My ^  11 and 5 b r i g h t e r than 8.5, i t i s of i n t e r e s t to see whether or not these r e s u l t s comply with estimates p r e d i c t e d from t h e o r e t i c a l c o n s i d e r a t i o n s . F o l l o w i n g F u s i - P e c c i and Re n z i n i (1979, h e r e a f t e r r e f e r r e d to as FPR), we can estimate N W D(<My), the number of white dwarfs b r i g h t e r than My i n a c l u s t e r , as: N W D ( < V = NHB ' t ( < V / 1 0 8 ( 4 ) where N ^ i s the number of h o r i z o n t a l branch s t a r s , t(<M v) i s the time i n years a 0.51 M @ white dwarf spends at l u m i n o s i t i e s b r i g h t e r than the l u m i n o s i t y corresponding to My, and 10 s years i s the t y p i c a l l i f e t i m e of a h o r i z o n t a l branch s t a r . FPR's a n a l y t i c a l f i t to Sweeney's (1976) c o o l i n g curve f o r 0.51 M^ white dwarfs y i e l d s : t(<M v) ~ 8.3 • 10 4 • 1 0 0 ' 3 2 < B C + V . (5) Lee (1977) found 153 h o r i z o n t a l branch s t a r s down to V = 14.6 w i t h i n 14.1' of the cente r of M4. His l i m i t i s about a magnitude below the mean p o s i t i o n of the h o r i z o n t a l branch; hence, h i s counts are reasonably complete f o r the region photometered. Although there may be f u r t h e r h o r i z o n t a l branch s t a r s l o c a t e d o u t s i d e of that area, they are expected to be comparatively few s i n c e 90% of the ones photometered 41 by Lee are w i t h i n approximately 10' from the c l u s t e r c e n t e r . Th e r e f o r e , adopting N U T 3 = 153, and bolometric c o r r e c t i o n s BC = -2.3 and BC -1 , f o r e f f e c t i v e temperatures of 25,000 K and 14,000 K, r e s p e c t i v e l y , N W D(<M V) can be d e r i v e d as a f u n c t i o n of M^ . as shown in Table V I I I . The number of white dwarfs from the t a b l e with My < 1 1 i s 201, which agrees q u i t e w e l l with the number of white dwarf c a n d i d a t e s found i n the b l i n k survey, although t h i s r e s u l t may be somewhat f o r t u i t o u s . R e c a l l i n g the f a c t that the b l i n k s t a t i s t i c s do not extend i n t o the c e n t r a l regions of the c l u s t e r where the d e n s i t y of white dwarfs i s expected to be the h i g h e s t , and a l s o the f a c t that the assumed background s u b t r a c t e d out to c o r r e c t the raw counts may have been an upper estimate ( s i n c e t h i s background was estimated w e l l w i t h i n the t i d a l r a d i u s of the c l u s t e r — l o g R = 1.64 as estimated by Peterson and King (1975)), the b l i n k survey r e s u l t must n e c e s s a r i l y be viewed as a lower l i m i t to the t o t a l number of white dwarfs more luminous than My = 1 1 i n the c l u s t e r . Even so, the numbers at l e a s t appear to be i n the r i g h t neighbourhood as p r e d i c t e d by theory. Table VII a l s o d i s p l a y s the number of white dwarfs with My < 8.5 expected in the c l u s t e r as about 12. T h i s i s s i g n i f i c a n t l y l a r g e r than the 5 observed photometric c a n d i d a t e s . Again, l o s s e s due to the aforementioned reasons may be manifest i n these r e s u l t s . An a l t e r n a t e p r e d i c t i o n of the number of white dwarfs in a g l o b u l a r c l u s t e r was d e r i v e d by H i l l s (1974). He 42 TABLE V I I I : PREDICTED NUMBER OF WHITE DWARFS IN M4 (FPR) T e f f = 2 5 ' 0 0 0 K ' B C = ~ 2 ' 3 T e f f = 1 4 ' 0 0 0 K ' B C = ~ 1 - 0 "v NWD ( < MV ) ^ NWD ( < MV } 7.0 4.1 10.0 96 7.5 5.9 10.5 139 8.0 8.5 11.0 201 8.5 12.2 11.5 291 9.0 17.7 12.0 421 9.5 25.6 12.5 608 10.0 37.0 13.0 879 accomplished t h i s by c a l c u l a t i n g the white dwarf c o n t r i b u t i o n to the UV region of the spectrum of a h y p o t h e t i c a l s t e l l a r system with an i n t e g r a t e d l u m i n o s i t y of L = 1 0 5 LQ. From h i s Table 2, the number of white dwarfs b r i g h t e r than a given My, can be expressed as a f u n c t i o n of m W D, the average white dwarf mass. I n t e r p o l a t i o n and i n t e g r a t i o n of h i s r e s u l t s gives Table IX which shows the number of white dwarfs b r i g h t e r than My = 8.5 (column 2) and My = 9.5 (column 3) expected in a t y p i c a l g l o b u l a r . I t i s apparent from t h i s t a b l e that the m W D = 0.6 M^ model with n e u t r i n o c o o l i n g i s the most c o n s i s t e n t with both the b l i n k survey and the photometry r e s u l t s — although, the probable incompleteness of the survey must once again be kept i n mind. 43 TABLE IX: PREDICTED NUMBER OF WHITE DWARFS IN M4 ( H i l l s ) mWD ( M © } NWD ( MV < 8' 5 ) NWD ( MV < 9' 5 ) 0.5 40.4 235 0.5" 24.8 359 0.6 30.1 162 0.6" 6.7 204 0.7 22.3 230 - models with n e u t r i n o emission Chapter 4 UV EXCESS QUASARS IN THE DIRECTION OF M4 4.1 SELECTION OF THE QSO SAMPLE From F i g u r e 9, i t i s evident that there i s a c o n t i n g e n t of o b j e c t s with c o l o u r s that are t y p i c a l of UV excess QSOs. More s p e c i f i c a l l y , the o b j e c t s with (U-B) 0 < -0.4, ( B - V ) 0 > 0.2, and are l o c a t e d above the blackbody l i n e , were c o n s i d e r e d to be good candidates f o r UV excess QSOs. These c r i t e r i a were chosen to d i s t i n g u i s h the QSO candidates from the white dwarfs and the subdwarfs. In f a c t , the remaining o b j e c t s photometered (the diamonds i n F i g u r e 9) that were not c l a s s i f i e d e i t h e r as a white dwarf or as a QSO, have c o l o u r s t y p i c a l of G subdwarfs and are t h e r e f o r e not i n t r i n s i c a l l y i n t e r e s t i n g i n t h i s a n a l y s i s . A t o t a l of 37 o b j e c t s met the QSO c r i t e r i a i n the 50' f i e l d and t h e i r d i s t r i b u t i o n i n h a l f magnitude i n t e r v a l s b r i g h t e r than B 0 i s t a b u l a t e d i n column 3 of Table X along with the l o g a r i t h m of that number per square degree in column 6. Because e r r o r s i n the photometry can a f f e c t the d i s t r i b u t i o n of the numbers in the b i n s , the a d j o i n i n g columns l a b e l l e d "max." and "min." i n d i c a t e the maximum and minimum number of QSOs i n each b i n should the photometry be in e r r o r by ±0.1 magnitudes. Since the l i m i t i n g B 0 magnitude of the photometry r e s u l t s i s 21, completeness can probably be claimed to t h i s magnitude. T h e r e f o r e , the l a s t b i n c o r r e s p o n d i n g to B 0 = 21.5 should be taken as a lower l i m i t . 44 45 TABLE X: QSO CANDIDATE NUMBER DISTRIBUTION B 0 n(<B 0) L 0 GN(<Bc,) degt max. min. max. min. 19.5 2 2 1 0.56 0.56 0.26 20.0 1 1 9 7 1 .30 1 .22 1.11 20.5 27 26 18 1 .69 1 .68 1 .52 21.0 36 34 33 1 .82 1 .79 1 .78 21 .5 37 37 36 1 .83 1 .83 1 .82 4.2 DISCUSSION OF THE RESULTS The data d i s p l a y e d i n Table X are presented i n F i g u r e 11 with the "max." and the "min." columns p r o v i d i n g the magnitude of the e r r o r bars. A c o l l e c t i o n of QSO i n t e g r a t e d s u r f a c e d e n s i t i e s compiled from s i m i l a r s t u d i e s ( M a r s h a l l et a l . 1983, Koo and Kron 1982, Schmidt and Green 1982, Kron and Chiu 1981, Usher 1978, and B r a c e s s i , F o r m i g g i n i , and G a n d o l f i 1970) employing the c o n d i t i o n of UV excess to d i s t i n g u i s h QSOs from g a l a c t i c s t a r s i s a l s o p l o t t e d i n the f i g u r e . The c o m p i l a t i o n i s by no means exhaustive and i s only meant to be r e p r e s e n t a t i v e of the r e s u l t s l i s t e d i n the l i t e r a t u r e . However, i t should be noted that the photometry from Koo and Kron and from Kron and Chiu was performed using t h e i r U, J , F, N system; and consequently, t h e i r c o l o u r c r i t e r i a f o r QSO s e l e c t i o n are s l i g h t l y d i f f e r e n t from the more c o n v e n t i o n a l d e f i n i t i o n s . A l s o , t h e i r QSO counts are d i s t r i b u t e d i n J r a t h e r than i n B. T h e i r c l a i m , however, i s that there i s l i t t l e to be l o s t in i n t e r p r e t i n g the J magnitudes d i r e c t l y as B magnitudes. The Koo and Kron data 46 CD U J O a c o CO C D o 2.8 2.4 2.0 1.6 1.2 0.8 0.4 0.0 -0.4 -0.8 -1.2 -1.6 -2.0 •2.4 o • Legend A BFG 1970 O MARSHALL et al. 1983 0 SCHMIDT & GREEN 1982 • KOO & KRON 1982 + USHER 1978 X KRON & CHIU 1981 • M4 FIELD QSOs LUM. EVOL. 16.0 17.0 18.0 19.0 20.0 21.0 22.0 23.0 24.0 B 0 FIGURE 11: QSO I n t e g r a t e d Surface D e n s i t i e s . N(<B 0) i s the number of QSOs per square degree b r i g h t e r than B 0. The s o l i d curve represents B r a c e s s i et a l . ' s (1980) pure l u m i n o s i t y e v o l u t i o n model. 47 i s a l s o unique i n s o f a r as t h e i r survey i s the deepest that has been completed to date. In f a c t , there i s a d e f i c i e n c y i n observed QSO s u r f a c e d e n s i t i e s f o r l i m i t i n g magnitudes f a i n t e r than B 0 - 20 and the survey of the M4 f i e l d QSO sample i s a c o n t r i b u t i o n towards s u p p l y i n g the much needed i n f o r m a t i o n . The s o l i d l i n e i n F i g u r e 11 i s the pure l u m i n o s i t y e v o l u t i o n model of B r a c e s s i et a l . (1980). I t seems to be q u i t e c o n s i s t e n t with the p l o t t e d data and has been so noted by M a r s h a l l et a l . and a l s o by Koo and Kron i n t h e i r surveys. The QSO c a n d i d a t e s in the M4 f i e l d a l s o appears to agree reasonably w e l l with t h i s model, which i s c h a r a c t e r i s t i c a l l y d i f f e r e n t from pure d e n s i t y e v o l u t i o n a r y models in i t s p r e d i c t i o n of the f l a t t e n i n g of the counts f o r l i m i t i n g magnitudes f a i n t e r than B 0 - 20. Chapter 5 CONCLUSIONS To summarize, an attempt has been made to l o c a t e a p o p u l a t i o n of white dwarfs i n the g l o b u l a r c l u s t e r M4. The search was s u c c e s s f u l in r e v e a l i n g a c o n c e n t r a t i o n in the number of UV b r i g h t o b j e c t s towards the c e n t e r of the c l u s t e r . Because there i s no reason to expect blue o b j e c t s such as QSOs, hot subdwarfs, or f a i n t blue g a l a x i e s to show high non-uniformity i n t h e i r d i s t r i b u t i o n over the M4 f i e l d , the r a d i a l c o n c e n t r a t i o n of the o b j e c t s appear to i n d i c a t e the presence of white dwarfs a s s o c i a t e d with the c l u s t e r . Support f o r t h i s h y p o thesis i s f u r t h e r enhanced when the background c o n t r i b u t i o n to the UV b r i g h t o b j e c t s was estimated and then s u b t r a c t e d from the o b j e c t counts. The r e s u l t i n g r a d i a l g r a d i e n t of the excess blue o b j e c t s agreed very f a v o r a b l y with that o b t a i n e d by King et a l . ' s (1968) s t a r counts i n M4. T h e r e f o r e , i t appears that the hot white dwarf component of M4 has indeed been observed, and an estimate of approximately 240 c l u s t e r white dwarfs b r i g h t e r than My 11 can be made f o r the region between 3.9' and 17.7' from the c l u s t e r c e n t e r . A number of the candidates were apparent on both the U and the B p l a t e s used f o r the b l i n k survey and these were photometered. The photometry y i e l d e d 12 c a n d i d a t e s with c o l o u r s i n d i c a t i v e of white dwarfs — 9 of which, have photometric p a r a l l a x e s c o n s i s t e n t with the c l u s t e r d i s t a n c e . Of these 9, 5 are b r i g h t e r than V = 21, the l i m i t i n g 48 49 magnitude of the photometered c a n d i d a t e s . T h i s s t r o n g l y i m p l i e s that 5 white dwarfs b r i g h t e r than My - 8.5 have been observed i n the b l i n k e d area of the M4 f i e l d . A comparison of these numbers with theory was made using F u s i - P e c c i and R e n z i n i ' s (1979) method of s c a l i n g the number of h o r i z o n t a l branch s t a r s by the r a t i o of a given 0.51 M Q white dwarf c o o l i n g time to the t y p i c a l l i f e t i m e of a h o r i z o n t a l branch s t a r . T h i s produced estimates of the t o t a l number of white dwarfs f o r the c l u s t e r as a whole, and t h e r e f o r e , cannot be d i r e c t l y compared to the r e s t r i c t e d r e g i on surveyed using the b l i n k comparator. N e v e r t h e l e s s , the p r e d i c t e d number of about 200 white dwarfs b r i g h t e r than My 11 and approximately 12 b r i g h t e r than My = 8.5 are i n the same order of magnitude as i n d i c a t e d by the o b s e r v a t i o n s . A second t h e o r e t i c a l r e s u l t was a l s o pursued using the estimates compiled by H i l l s (1974) i n h i s m o d e l l i n g of the white dwarf c o n t r i b u t i o n to the spectrum of a t y p i c a l 10 5 L Q s t a r system. His 0.6 M @ white dwarf model with n e u t r i n o c o o l i n g g i v e s p r e d i c t e d v a l u e s of the same order of magnitude ( i . e . =* 7 f o r My < 8.5 and ^ 200 f o r My < 9.5) as the F u s i - P e c c i and R e n z i n i estimates; a l b e i t , once again , they are f o r the e n t i r e c l u s t e r r a t h e r than f o r the s e l e c t e d r e g i o n . T h e r e f o r e , although the present o b s e r v a t i o n s cannot be u t i l i z e d f o r r i g o r o u s l y d i s t i n g u i s h i n g between t h e o r e t i c a l models, they are, at l e a s t , not d i s s i m i l a r to the general p r e d i c t i o n s . T h i s lends yet a d d i t i o n a l support to the c l a i m f o r the d i s c o v e r y of a 50 hot white dwarf component i n M4. A secondary f i n d i n g concerns the i n v e s t i g a t i o n of the su r f a c e d e n s i t i e s of UV excess QSOs i n the f i e l d of M4. A t o t a l of 37 o b j e c t s photometered showed c o l o u r s t y p i c a l of UV excess QSOs and t h e i r i n t e g r a t e d number d e n s i t y d i s t r i b u t i o n from B 0 = 19.5 to B 0 = 21.5 was found to be q u i t e c o n s i s t e n t with the B r a c e s s i et a l . (1980) model. T h i s model assumes a pure l u m i n o s i t y e v o l u t i o n of the quasar p o p u l a t i o n and p r e d i c t s a f l a t t e n i n g of the QSO counts f a i n t e r than B 0 =* 20. Other recent surveys (e.g. Koo and Kron 1982 and M a r s h a l l et a l . 1983) have a l s o r e v e a l e d t h i s t r e n d and the M4 f i e l d QSO r e s u l t f u r t h e r supports t h i s view. BIBLIOGRAPHY Anthony-Twarog, B. J . 1982, Ap. J., 255, 245. B r a c e s s i , A., F o r m i g g i n i , L., and G a n d o l f i , E. 1970, A s t r o n . & As t r o phys. , 5, 264. B r a c e s s i , A., Z i t e l l i , V., B o n o l i , F., and F o r m i g g i n i , L. 1980, Astron. & Aslrophys., 85, 80. F u s i - P e c c i , F., and R e n z i n i , A. 1979, i n Proc. ESA/ESO Workshop on Astronomical Uses of the Space Telescope. , F. Macchetto, F. P a c i n i , and M. Tarenghi, eds. (Geneva), p. 181. Green, R. F. 1980, Ap. J., 238, 685. H i l l s , J . G. 1974, Ap. J., 190, 109. Koo, D. C., and Kron, R. G. 1982, Astron. & Astrophys., 105, 107. Kron, R. G. 1980, Ap. J. Suppl. Ser., 43, 305. Kron, R. G., and Chiu L. T. G. 1981, Pub. A. S. P. , 93, 397. King, I. R., Hedemann, E., and Hodge, S. M. 1968, A. J., 73, 456. Lee, S.-W. 1977, Astron. & Astrophys. Suppl. Ser., 21, 367. Matthews, T. A., and Sandage, A. R. 1963, Ap. J., 138, 30. M a r s h a l l , H. L., Tananbaum, H., Zamorani, G., Huchra, J . P., B r a c e s s i , A., and Z i t e l l i , V. 1983, Ap. J., 269, 42. N i c o l , J . S. 1984, i n t e r n a l document, i n p r e p a r a t i o n . Peterson, C. J . , and King, I. R. 1975, A. J., 80, 427. Racine, R. 1971, Ap. J., 168, 393. Romanishin, W., and Angel, J . R. P. 1980, Ap. J., 235, 992. R i c h e r , H. B. 1978a, Ap. J. , 224, L9. R i c h e r , H. B. 1978b, Ap. J. , 226, L157. R i c h e r , H. B. 1979, i n White Dwarfs and Variable Degenerate S t a r s , H. M. Van Horn and V. Weidemann, eds. (Rochester: U n i v e r s i t y of Rochester P r e s s ) , p. 259. Ri c h e r , H. B., and Fahlman, G. G. 1984, Ap. J., 277, 277. 51 52 Ric h e r , H. B., and Fahlman, G. G. 1985, Ap. J., i n pr e s s . Schmidt, M., and Green, R. F. 1982, i n Ast r o p h y s i c a l Cosmology: Proc. Vatican Study Week on Cosmology and Fundamental Physics., H. A. Bruck, G. V. Coyne, and M. S. Lo n g a i r , eds. (Rome: Specola V a t i c a n a ) , p. 281. Shipman, H. L. 1972, Ap. J. , 177, 723. Shipman, H. L. 1979, Ap. J. , 2 2 8 , 240. Sweeney, M. A. 1976, Astron. & Astrophys., 49, 375. Usher, P. D. 1978, Ap. J., 2 2 2 , 40. APPENDIX I: ESTIMATE OF THE WD FOREGROUND Assume that G a l a c t i c white dwarfs are d i s t r i b u t e d i n f l a t , uniform d e n s i t y d i s k s bounded by s c a l e h e i g h t s dependent upon the i n t r i n s i c b r i g h t n e s s e s of the white dwarfs. I n t e r s t e l l a r a b s o r p t i o n i s assumed to be c o n f i n e d to the plane of the galaxy with a s c a l e height much l e s s than those of the white dwarfs. The number of white dwarfs N(R,My), of absolute v i s u a l magnitude My, out to a d i s t a n c e R, i n an area of sky subtended by a s o l i d angle u>, i s then: N(R,My) = </>(My) u r 2 dr (A1 ) where tf>(My) i s the space d e n s i t y of white dwarfs with l u m i n o s i t y My. Since 1 s r . = (7r/18 0 ) 2 deg?, i n t e g r a t i o n of equation (A1 ) g i v e s : N(R,My)/deg? = (TT/180) 2 • 0(My) • R 3/3. (A2) For R w i t h i n the d i s k boundaries, the f o l l o w i n g can be s u b s t i t u t e d i n t o equation (A2): R - 1 0 0 ' 2 ( V " V + \ (A3) g i v i n g , with i n t e g r a t i o n over V on the i n t e r v a l (-°°,V0], N(<V,My)/deg 2 = ( 5000/9) • ( TT/1 8 0 ) 2 • tf>(My) • I D 0 ' 6 ( V ° - V . (A4) 53 54 A f i n a l i n t e g r a t i o n over My g i v e s the number of white dwarfs b r i g h t e r than the dereddened l i m i t i n g magnitude V 0 as: N(<V)/deg? = ( 5 0 0 0 / 9 ) - ( 7 r / l 8 0 ) 2 . l 0 0 - 6 V ° ./JJj 0(My) • 1 0 " 0 ' 6 dMy (A5) where M, and M 2 are, r e s p e c t i v e l y , the low and the high l u m i n o s i t y c u t o f f s of <>(My). The observed l u m i n o s i t y f u n c t i o n f o r hot s o l a r neighbourbood white dwarfs (9.75 < My < 13.25) of Green's (1980) survey can be used i n the above equations to p r e d i c t the number of white dwarfs i n the f i e l d of M4 down to a given l i m i t i n g magnitude. For V 0 = 20, however, R f o r the h o t t e s t white dwarfs surveyed by Green (9.75 < My < 10.25), c a l c u l a t e d by equation (A3), exceeds the d i s t a n c e to the edge of the white dwarf d i s k i n the d i r e c t i o n of M4. T h e r e f o r e , equation (A5) i s not a p p l i c a b l e i n t h i s case. However, equation (A2) can be used i f R i s taken to be the d i s t a n c e to the d i s k edge ( a r r i v e d at by using the a p p r o p r i a t e s c a l e height from Green's b e s t - f i t model and the g a l a c t i c l a t i t u d e of M4). The number of white dwarfs with 9.75 < My < 10.25 i n the 50' diameter f i e l d of M4 i s then found to be about 1.0. For white dwarfs with 10.25 < My < 13.25, equation (A5) i s a p p l i c a b l e and the number i n the f i e l d i s found to be approximately 7.3. T h e r e f o r e , the t o t a l number of hot foreground white dwarfs expected to be 55 observed i n the M4 f i e l d down to a l i m i t i n g magnitude of V 0 =« 20 i s approximately 8. S i m i l a r l y , an estimate of the number of f i e l d white dwarfs i n the foreground down to V = 23.5 ( i . e . V 0 = 22.5) can a l s o be determined. C a l c u l a t i o n s show that a t o t a l of about 80 can be expected over the f i e l d down to t h i s l i m i t i n g magnitude (or about 0.04 per square minute of a r c ) . APPENDIX I I : FINDING CHARTS FOR THE PHOTOMETERED CANDIDATES The p o s i t i o n s of the 74 photometered UV b r i g h t c a n d i d a t e s are i n d i c a t e d on the f i n d i n g c h a r t s A — E in F i g u r e s 12 — 16. North and east are a l s o i n d i c a t e d on these c h a r t s ; east i s to the l e f t when the c h a r t s are o r i e n t e d so that north i s up. A p o r t i o n of the M4 f i e l d with dimensions of about 24' x 32' i s d i s p l a y e d i n each of the c h a r t s except f o r f i n d i n g c h a r t E, where a re g i o n of approximately 12' x 16' about the c l u s t e r c e n t e r i s shown. F i g u r e 17 i n d i c a t e s the o r i e n t a t i o n s and l o c a t i o n s of each of the f i n d i n g c h a r t s in the f i e l d of M4. In t h i s f i g u r e , north i s up and east i s to the l e f t . 56 FIGURE 12: F i n d i n g Chart St N ^675 •^-671 -86 ^687 -.-810 • . ' "* :'• ' •> « - ~ 6 . 5 9 ' .'696 • - - g o .. % - - - 6 9 5 340 • ' : %699 -.' . • • 653 • %' r. . 702 _ ^772-- • .V... > • >• - - 7 7 0 - / -• • '• • • , •: • i \ '• ••>••.••• ?;v^ ... .. . •. . y,. •* . • ,1 • ». . * ,*••*..*«-• ' •*•'*-. : P ** *• - - 9 8 . • • • .497 ;--710 * ^rs^t-r.y,.:'"?/ •644. • ~" >. • . •.-•."•>• FIGURE 13: F i n d i n g Chart N ^1305 ^1187 ^36 ' • .' . ^1314. - - 1 2 9 1 7 ^ t .1042 \ v 942v . . - - 1 3 2 0 .«. .•• - -1699 ^ - 1 7 4 7 o FIGURE 14: F i n d i n g Chart C. FIGURE 15: F i n d i n g Chart 494 • • / • •.• . . : '." 102©'. ^ 5 9 1 '.' % r : r-973 : r - ' : . ' : - : - - - ' . ' - - : - i > H -. • ;•;../•, --974 - •.. - - v. ~1138 -407 • -595 --'724 :981 , \ • M 2 3 1 • - «m ; * ' 1 0 0 9 6 0 1 - - 7 4 8 • • ' 604 _853 „ 8 7 0 - " 4 7 5 _^988 . » > ' - -731 FIGURE 16: F i n d i n g Chart 67 FIGURE 17: L o c a t i o n of the F i n d i n g Charts A -E. North i s up and east i s to the l e f t . 

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